Year 8 Maths strengthens the transition from arithmetic into formal algebra, mathematical modelling and geometric reasoning. Students work with irrational numbers, exponent laws, linear relations, measurement, Pythagoras, congruence, sampling and probability while learning to explain and justify their methods.

Key Topics Covered:

Irrational and rational numbers, exponent laws, percentages and financial mathematics, linear expressions and equations, linear graphs, area and volume, circles, time zones, rates and ratios, Pythagoras, congruence and similarity, 3D coordinates, sampling, statistics and probability.

Parent Tip:

Year 8 is a major algebra foundation year. Students who become confident with linear expressions, equations, graphs, ratio and Pythagoras now are much better prepared for the quadratic and trigonometric work introduced in Year 9.

Work confidently with rational and irrational numbers and exponent laws

Create, simplify, expand and factorise linear expressions and solve equations and inequalities

Graph and model linear relations in practical and financial contexts

Solve measurement problems involving composite shapes, circles, prisms, rates and time

Apply Pythagoras, congruence, similarity and coordinate reasoning to spatial problems

Collect, analyse and interpret samples and use probability to reason about chance

Student graphing linear relations for Year 8 maths online with a tutor in Australia

No.	Topic	What We Cover
01	Irrational Numbers, Square Roots and Pi	Recognise irrational numbers in applied contexts; locate approximations on the real number line and connect square roots and pi to practical geometry.
02	Exponent Laws	Establish and apply product, quotient, power-of-a-power and zero-exponent laws with positive integer exponents.
03	Terminating and Recurring Decimals	Recognise terminating, recurring and non-terminating decimals and connect decimal behaviour to fractional representations.
04	Operations with Integers	Use all four operations with positive and negative integers, selecting efficient strategies and explaining the effect of signs.
05	Operations with Rational Numbers	Apply the four operations to fractions and decimals, using efficient written, mental and digital strategies.
06	Percentages and Percentage Change	Solve percentage increase and decrease problems including mark-ups, discounts, GST and population or environmental change.
07	Financial Mathematics and Modelling	Model practical financial situations involving tax, rates, income and percentage change; interpret and communicate solutions.
08	Linear Expressions: Simplifying and Rearranging	Create, rearrange and simplify linear expressions using associative, commutative, identity and inverse properties.
09	Expanding and Factorising Linear Expressions	Apply the distributive property to expand and factorise linear expressions and explain the inverse relationship between the processes.
10	Term 1 Number and Algebra Review	Integrate real numbers, exponents, rational-number operations, percentages and introductory algebra in multi-step problems.

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Student in a tutoring session with their tutor

Warm-up (5 min)

Quick mental maths and a review of the previous session

Core Teaching (25 min)

New concept from the lesson eBook, with examples and guided practice

Guided Practice (15 min)

Student works through problems with tutor support

Independent Practice (10 min)

Student completes the in-class quiz independently

Wrap-up (5 min)

Summary, 2 take-home quizzes and a preview of the next session

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No.	Topic	What We Cover
11	Linear Equations	Solve linear equations algebraically using inverse operations and verify solutions by substitution.
12	Linear Inequalities	Solve one-variable linear inequalities and represent solution sets graphically and on number lines.
13	Tables, Graphs and Linear Relations	Generate tables of values, plot linear relations on the Cartesian plane and recognise constant first differences.
14	Gradient and Initial Value in Context	Interpret constant rate of change and initial value in practical linear models such as fares, pay rates and motion.
15	Linear Modelling	Formulate and solve applied problems using linear functions; select representations and judge whether solutions are sensible in context.
16	Exploring Linear Functions Digitally	Vary parameters of linear functions and inequalities with digital tools; make, test and generalise conjectures about graphs.
17	Area and Perimeter of Composite Shapes	Solve problems involving perimeter and area of irregular and composite shapes by decomposing or approximating regions.
18	Volume and Capacity of Right Prisms	Solve practical problems involving volume and capacity of right prisms and convert appropriately between cubic units, millilitres and litres.
19	Circles: Circumference and Area	Apply formulas for circumference and area of circles and deduce unknown radius, diameter, circumference or area.
20	Term 2 Algebra and Measurement Review	Apply linear relations, equations, inequalities, area, volume and circle measures in mixed reasoning problems.

No.	Topic	What We Cover
21	Duration and Time Zones	Solve duration problems using 12- and 24-hour time across multiple time zones, including daylight-saving and travel contexts.
22	Rates and Unit Rates	Recognise and use rates to compare quantities with different units, including pay, cost, speed, consumption and exchange rates.
23	Pythagoras' Theorem	Use Pythagoras' theorem to determine unknown side lengths in right-angled triangles and solve practical distance problems.
24	Ratios, Proportion and Scale	Solve ratio and proportion problems involving maps, plans, mixtures, magnification and scale factors.
25	Mathematical Modelling with Ratios and Rates	Formulate practical and financial models involving ratios and rates, interpret results and review the appropriateness of the model.
26	Congruence of Triangles	Identify conditions for triangle congruence and use logical reasoning to justify when shapes are congruent.
27	Similarity and Transformations	Identify similarity conditions and connect enlargement, reflection, rotation and translation to properties that change or remain invariant.
28	Quadrilateral Properties and Reasoning	Establish and apply properties of squares, rectangles, parallelograms, rhombuses, trapeziums and kites using angles, sides and diagonals.
29	Three-Dimensional Coordinates	Describe position and location in three dimensions and compare 2D and 3D coordinate systems using digital tools.
30	Algorithms for Congruence and Similarity	Design, create and test step-by-step algorithms or flow charts that classify shapes as congruent or similar.

No.	Topic	What We Cover
31	Data Collection: Census, Sampling, Experiments and Observation	Compare data-collection techniques and discuss practicality, precision, bias and implications of different methods.
32	Random and Non-Random Sampling	Analyse data from primary and secondary sources and compare random, systematic, stratified, quota, cluster and convenience sampling.
33	Sample Variation and Sample Size	Compare distributions and proportions from repeated random samples and investigate how sample size affects variation.
34	Measures of Centre and Spread in Samples	Use mean, median and range to compare samples and investigate the impact of adding, removing or changing data.
35	Probability: Sample Spaces and Events	Represent chance situations systematically and use probability language and sample spaces to reason about outcomes.
36	Compound Events and Representations	Use lists, tables, arrays, tree diagrams or other representations to organise multi-step chance events and determine probabilities.
37	Experimental Probability and Relative Frequency	Use repeated trials and relative frequency to estimate probabilities and compare experimental results with theoretical expectations.
38	Probability Simulations with Digital Tools	Design and run simulations to investigate chance, sample variation and long-run behaviour.
39	Integrated Statistics and Probability Investigation	Plan a data or chance investigation, select appropriate representations, analyse results and communicate justified conclusions.
40	End-of-Year Year 8 Mathematics Assessment	Complete an integrated assessment across Number, Algebra, Measurement, Space, Statistics and Probability using multi-step and modelling problems.

Year 8 Maths Tutoring in Australia

By Term 4 of Year 8 Maths, Your Child Will...

Year 8 Maths Curriculum, Term by Term

Try a Free Lesson to See the Full Program

Try a Free Lesson to See the Full Program

Try a Free Lesson to See the Full Program

Try a Free Lesson to See the Full Program